A detectable event is herein defined as a loss or gain of one or several positioning satellites (and/or pseudolites) and a loss or gain of a differential correction signal that lead to undesirable user position biases. If user's initial position coordinates were determined by using a Weighted Least Squares (WLS) solution, these biases would appear in the form of instantaneous jumps in the Weighted Least Squares (WLS) solution. If, on the other hand, an initial position coordinates were determined by using a Kalman Filter (KF) solution, the biases would appear in the form of drifts in the Kalman Filter (KF) solution. As a result, in both situations, the positioning becomes problematic in various types of applications.
For instance, on an agricultural field, when user is trying to maintain long, parallel and straight swaths that are tightly close to one another, these position biases occur causing the vehicle to divert from its straight line path. Although, a bias might lead to a more accurate position in the absolute sense, in the agricultural (and many other applications) what is important is a relative position accuracy defined in a reference to an initial position accuracy determined at the end to a selected initial Epoch at which an initial position and its accuracy were determined by using an initial satellite (and/or pseudolites) constellation and an initial differential signal status. This initial Epoch's constellation and the initial differential signal status are hereafter referred to as truth, and all events that occur after it are considered to be problematic as all these events create biases that should be eliminated.
To deal with this task, in the case of WLS, a Position Bias Filter (PBF) was implemented in the position domain. The PBF simply tracks and calculates the WLS position biases caused by every event and accumulates them in a position bias vector that is removed from the WLS solution's position vector.
However, a PBF cannot be used with a KF solution because the KF diffuses the instantaneous position jumps, encountered in WLS, into drifts over the course of several Epochs, making it difficult to assess the biases in the position domain during these Epochs.